Factor.t2–11t+24

Sure, here is the step-by-step solution to factor the quadratic equation t^2 - 11t + 24:

Step 1: Write down the equation t^2 - 11t + 24 = 0

Step 2: Identify the coefficients of t^2, t, and the constant term. In this case, they are 1, -11, and 24 respectively.

Step 3: We need to find two numbers that multiply to 24 (the constant term) and add up to -11 (the coefficient of t). The numbers that satisfy these conditions are -8 and -3 because -8*-3 = 24 and -8 + -3 = -11.

Step 4: Rewrite the middle term of the equation as the sum of the terms -8t and -3t. t^2 - 8t - 3t + 24 = 0

Step 5: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. t(t - 8) - 3(t - 8) = 0

Step 6: Notice that (t - 8) is a common factor. Factor out (t - 8). (t - 8)(t - 3) = 0

So, the factored form of the equation t^2 - 11t + 24 = 0 is (t - 8)(t - 3) = 0.